In studying fertility, demographers generally focus on the mean number of children born, whether cumulatively or within an interval of age or marital duration. Although this is of course the single most important measure, it is an incomplete description of the full distribution. The mean can decline through a reduction in the frequency of large families, or through an increase in the frequency of zero or one-child families, or through both changes. These changes have different implications for labor force participation, household structure, etc. Changes in the distribution can occur even when the mean does not change. This project's goal is to improve upon our ability to describe the distribution of family size across the childbearing ages, and our ability to relate it to cohort differences and socio-economic characteristics. Five specific aims are included: (1) establishment of a data base, (2) development of parametric models and estimation procedures, (3) development of classificatory models, (4) incorporating the effect of covariates, and (5) development of desired family size distributions. In pursuing these, strategies will be employed which others have successfully applied to age-specific patterns of mortality, fertility, and nuptiality. For example, the data base of observed distributions will be reduced to one or more prototypical patterns to which others can be related by transformations. It is expected that several types will emerge; the empirical groupings can be related to the macro-level characteristics of the distributions. A major effort will go into the development of one or more parametric models. These will apply functional forms, primarily to the parity progression ratios and logit transformations thereof, in order to capture efficiently the main features of the entire distribution in two or three coefficients. The end result will be much more sensitive indicators of variations and changes in family-building than are presently available.